Is it possible to join Indian navy after passing 12th grade with science stream examination??

Yes you can join Indian navy after passing 12th grade with science stream examination through NDA examination organized by UPSC ..

Here I am giving you information about required eligibility for National defense academy examination

Eligibility:
For Air Force and Naval Wings of National Defence Academy
You should be 10+2 passed with physics and mathematics subjects. Candidates who are appearing in the 12th class under the 10+2 pattern of school education or equivalent can also apply.

For Army wing of National Defense Academy
You have to passed 12th Class of 10+2 pattern of School Education or equivalent examination conducted by a State Education Board or a University.

Age limit :
The candidate’s minimum age is 16 1/2 years and maximum age 19 years for the NDA exam.

Sex:
Only unmarried male candidates are eligible.

(a) Nationality:
A candidate must either be:
A citizen of India, or
A subject of Bhutan, or
A subject of Nepal, or
A Tibetan refugee who came over to India before the 1st January, 1962

Exam Dates
Date of notification : 21 JUNE 2014
Last date of form submission : 21 JULY 2014
Date of NDA exam is 28th SEPTEMBER 2014